Ajunk box in your room contains fourteen old batteries, seven of which are totally dead. you start picking batteries one at a time and testing them. find the probability of each outcome. a) the first two you choose are both good. b) at least one of the first three works. c) the first four you pick all work. d) you have to pick five batteries to find one that works.

A junk box in your room contains fourteen old batteries, seven of which are totally dead.

So, number of good batteries =

a) The first two you choose are both good.

There is a 7/14 chance that we will pick a good battery.

Now there are 13 batteries left and out of that there are only 6 good ones remaining, so this becomes 6/13.

So, combined probability is =

= 0.23

b) At least one of the first three works.

And at least one is good battery, we get :

c) The first four you pick all work.

There is a probability of 7/14 for the first one to work, 6/13 for the second, 5/12 for the third and 4/11 when the fourth is good, combined we get by multiplying all:

d) You have to pick five batteries to find one that works.

This condition means that we pick 4 bad batteries and 1 good battery.

The probability of picking 4 bad batteries is -

Since there are 7 good batteries remaining in 10 batteries so we will multiply 7/10 in 0.0344 to know the fifth one that finally works.  

This becomes =